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Supersymmetry Breaking Triggered by Monopoles
David Curtinbla
arXiv:1108.4415
In collaboration with Csaba Csáki [Cornell],Vikram Rentala [U. Arizona],In collaboration wih Yuri Shirman [UC Irvine], John Terning [UC Davis]
SUSY ’11 Parallel TalkFermilab
August 28, 2011
Motivation
Always looking for new ways to break SUSY.
→ The unique characteristics of dynamical monopoles makes themworthy of investigation in this context.
- Seiberg-Witten methods allow us to find theories with masslessmonopoles and/or dyons, and include them in model building.
Light monopoles might play a role in electroweak symmetrybreaking (Csaki, Shirman, Terning 2010)
−→ Problems with calculablity. Toy Models?
Stony Brook University David Curtin ��SUSY Triggered By Monopoles 1 / 15
(Very) Brief Review:
Seiberg-Witten Analysis
ofN = 2 SU(2) SYM
N = 2 SU(2) SYM (Seiberg, Witten 1994)
Aa
λa ψa
φa
D-flat: [φ†, φ] = 0 =⇒ Moduli Space parameterized by u = 12 Trφ2. SU(2)→ U(1)
Seiberg-WittenAnalysis
Near monopole singularity: U(1)mag with Weff ≈ (u − Λ)MM.
Stony Brook University David Curtin ��SUSY Triggered By Monopoles 2 / 15
Upshot
Can exactly solve for low-energy theory of N = 2 SU(2) SYM.
→ generalizes to SU(N) with fundamental flavors ( , ¯ hypers)
→ cool stuff at higher rank: SU(3) SYM can have simultaneouslymassless electric & magnetic charges! (Argyres-Douglas Point)
Can softly break to N = 1 to learn about nontrivial N = 1physics, e.g. gaugino condensation as magnetic Meissner effect.
These methods can give us some information even in N = 1theories.
Stony Brook University David Curtin ��SUSY Triggered By Monopoles 3 / 15
Application of SW Methods
to N = 1 Theories
↓
The SU(2)3 Model
Application to N = 1 SUSY (Intriligator, Seiberg ’94)
Apply SW methods to N = 1 theories in the Coulomb phase.
Can calculate the following as a function of the moduli:
- holomorphic low-energy U(1) gauge coupling τeff . If singular, weknow there are light monopoles or dyons!
- effective superpotential near the singularity.
Cannot calculate
- explicit masses for monopoles/dyons.
- Kähler potential
This allows us to identify N = 1 theories with light monopoles anddyons, and learn something about their low-energy behavior.
Stony Brook University David Curtin ��SUSY Triggered By Monopoles 4 / 15
SU(2)3 Model (Csaki, Erlich, Freedman, Skiba ’02)
SU(2)1 SU(2)2 SU(2)3Q1Q2Q3
4 moduli space coordinates:
Mi = QiQi
T = Q1Q2Q3
Similar to N = 2 SU(2) SYM: When
Λ41M2 + Λ4
2M3 + Λ43M1 −M1M2M3 + T 2 −→ ±2Λ4
1Λ42Λ4
3
magnetic or dyonic charges become massless, elementary andweakly coupled.
Near monopole singularity, the effective superpotential is
Weff =
[−M1 −M2 −M3 +
M1M2M3
Λ2 − T 2
Λ+ 2Λ
]E+E+
(Rescaled moduli, and set Λi = Λ for simplicity.)Stony Brook University David Curtin ��SUSY Triggered By Monopoles 5 / 15
Effective TheoryTo analyze SUSY-breaking, we need to parameterize ourignorance of the Kahler potential.
To restrict Kahler using global symmetries, expand aroundparticular point in moduli space:
M1 = 2Λ + δM1, M2 = δM2, M3 = δM3, T = δT .
A global Z4 symmetry (Mi , T charge 1, 2) is broken to Z2. Thisforbids δMiδT Kahler mixing at quadratic order.
It is possible to define (approximately) canonical fluctuations Miaround M1 = 2Λ. The effective superpotential becomes
Weff =
[aM1 + bM2 + cM3 − d
T 2
Λ+ H.O.T.
]E+E+.
Can this theory be modified to break SUSY?
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Shih model ofSUSY breaking
Shih’s O’Raifeartaigh model (2008)
We will deform the SU(2)3 theory to become this model in alow-energy limit.
generalized O’Raifeartaigh model with R-charges other than 0,2,which can break R-symmetry without tuning.
W = X (f + λφ1φ2) + m1φ1φ3 + 12m2φ
22
- This is generic for RX = 2,Rφ1 = −1,Rφ2 = 1,Rφ3 = 3.
- Two dimensionless parameters control whether SUSY andR-symmetry can be spontaneously broken in a metastablevacuum:
y =λf
m1m2, r =
m2
m1,
Stony Brook University David Curtin ��SUSY Triggered By Monopoles 7 / 15
Minimizing the scalar potential
For y < 1, there exists a stable SUSY-breaking pseudomodulispace
φi = 0 , X = undetermined at tree-level with |X | < Xmax
1-loop quantum corrections generate VCW(|X |):
1 2 3 4x�
0.002
0.004
0.006
0.008V�cw
r � 1.5 , y � 0.20
0.5 1.0 1.5 2.0 2.5x�
�0.0004�0.0002
0.00020.00040.00060.0008
V�cw
r � 4.0 , y � 0.20
There is also a SUSY-runaway→ metastable ����SUSY.
Stony Brook University David Curtin ��SUSY Triggered By Monopoles 8 / 15
������SUSY and ��R
For y < 1, the Shih-model can exhibit����SUSY. For r >∼ 2, also have��R.
〈X〉 in units of√
f/λ
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Scaling Behavior of VCW
The deformed SU(2)3 model will resemble the Shih-model up touncalculable corrections.
To ensure that the false vacuum is not destabilized we have tounderstand how the 1-loop potential scales. Numerically we find
y < ymax ≈ 2/r for���SUSY
〈X 〉 ≈ (1− y2) m24λ
mX ∼ 13
√λ5f 3
m1m2[∆V
∆|X |
]max∼ 1
8π2λ3f 2
m2
↑ This indicates how robustly the pseudomodulus X is stabilized.
Stony Brook University David Curtin ��SUSY Triggered By Monopoles 10 / 15
SUSY-Breaking triggered byMonopole Condensation
Deforming the SU(2)3 model
We will deform the SU(2)3 model to get an effective Shih modelof metastable ����SUSY.
→ We would like the ����SUSY to vanish in the absence of a monopolecondensate.
Consider SU(2)3 model around M1 = 2Λ:
Weff ≈
[aM1 + bM2 + cM3 − d
T 2
Λ
]E+E+.
Add some tree-level terms and extra SU(2)3 singlet fields:
δW = −µ2M1+λM2φ1φ2 +12
m2φ22 + m1φ1φ3+mZ ZT + mY M3Y
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������SUSY Mechanism
Weff ≈[aM1 + bM2 + cM3 − d
T 2
Λ
]E+E+
−µ2M1 + λM2φ1φ2 +12
m2φ22 + m1φ1φ3
+mZ ZT + mY M3Y
FM1→ 〈E+E+〉 ∼ µ2 ⇒ M2 gets a tadpole ∼ 〈E+E+〉 ∼ µ2.
(spectator moduli are stabilized by giving them a mass withsinglets)
⇒ effective Shih-model with X → M2, f → ∼ 〈E+E+〉
Metastable SUSY-breaking triggered by monopolecondensation!
Stony Brook University David Curtin ��SUSY Triggered By Monopoles 12 / 15
Electric TheorySU(2)1 SU(2)2 SU(2)3
Q1Q2Q3
SU(2)’s become strongbelow scale Λ
Wtree = m(QQ)A +λ
ΛUV(QQ)Bφ1φ2 +
12
m2φ22 + m1φ1φ3
+aZ
ΛUVQ1Q2Q3Z + ay (QQ)CY , (ΛUV � Λ)
To ensure vacuum stability,
- (QQ)A,B,C are linear combinations of Q21 ,Q
22 ,Q
23 and Λ2 that become
canonical Mi in the IR. Have to be lined up to a precision of∼ 10−2 − 10−3,
- Stability against Kähler corrections requires m� m1,2 � Λ� ΛUV
Λ→ 0 restores SUSY.
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Other DeformationsIt is instructive to embed the Shih model differently into SU(2)3.
Weff ≈[aM1 + bM2 + cM3−d
T 2
Λ
]E+E+
Composite φ2 instead of pseudomodulus X :
δW = −f M1 + X (λTφ1 − µ2)+m1φ1φ3+mZ ZM2 + mY M3Y
No Good: Not dynamical ����SUSY.
Composite φ2 and pseudomodulus X :
δW = −f M1 + λM2Tφ1 + m1φ1φ3+mY M3Y
No Good: Cannot guarantee stability of vacuum.
Nevertheless, this method of constructing monopole modelsthat break N = 1 SUSY should be fairly general.
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Conclusion
Conclusion
Seiberg-Witten methods give us a handle on topologicalmonopoles and open up new model-building possibilities.
We show that metastable SUSY-breaking can be triggered bymonopole condensation.
These strategies should make it possible to induceSUSY-breaking in a variety of models in the Coulomb phase byobtaining different low-energy ����SUSY models.
→ Lots of things one could try!
It would be very interesting to try and break SUSY in theorieswith light electric and magnetic charges.
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